Online Bayesian dictionary learning for large datasets

The problem of learning a data-adaptive dictionary for a very large collection of signals is addressed. This paper proposes a statistical model and associated variational Bayesian (VB) inference for simultaneously learning the dictionary and performing sparse coding of the signals. The model builds upon beta process factor analysis (BPFA), with the number of factors automatically inferred, and posterior distributions are estimated for both the dictionary and the signals. Crucially, an online learning procedure is employed, allowing scalability to very large datasets which would be beyond the capabilities of existing batch methods. State-of-the-art performance is demonstrated by experiments with large natural images containing tens of millions of pixels.